There are so many games that I loved to play in browsers. Some are gone now I think, but I will talk about them anyway, as well as games that have changed or that I don't know if they are still the same (we are talking decades now that I'm so old).
2000s:
-NabiscoWorld Minigolf (and related flash games): I loved these games. I just thought the play control and the gimmicks were really smartly done. I think this is still playable somehow, but I don't know how.
-Need for Madness: Absolutely my favorite racing game, or one of them at least. I loved the gameplay and the music. The sequel isn't bad either.
-Winterbells: Just a peaceful and fun infinite jump game
-Nanaca CRASH!: Hilarious game and tons of fun. Still running on an official mirror site.
-Miniclip Motobike: A weird game that was like motocross maniacs but with more flexibility (and more ways to fail). Very similar to Joe Danger, Trials, and other such "wacky neck-breaking simulators".
-Curveball: A 3D pong where you could put spin on the ball based on how you hit the ball
2010s:
-Bonk.io: I still have some fun with this game on occasion. It's just enjoyable to manipulate the physics. I wish it had a little less gimmick maps, as they aren't really that interesting past the first time or two that you see them
-Realm of the Mad God: I LOVED this game like 10 years ago, but once they started adding facebook integration and in-game purchases I stopped playing it. I would love a game that was similar but without the pay crap.
-Meme games: Winnie the Pooh Home Run Derby and Spongebob Boat-o-Cross were hilarious.